Thread: Parallel Transport (Plane)

I'm just wondering what parallel transport in the plane mean. I drew the following picture:
So does Parallel Transport say that a=a* and b=b*?

Any help would be greately appreciated.

Originally Posted by statmajor

I'm just wondering what parallel transport in the plane mean. I drew the following picture:
So does Parallel Transport say that a=a* and b=b*?

Any help would be greately appreciated.

I am not familiar with that term, but if ab is parralel to a*b*, then a and a* and b and b* have the same angle.

I'm trying to prove that a=a* and b=b* using only the fact that the sum of the interior angles of a triangle is 180 degrees.

In my diagram, there are 2 triangles: ABC and A*B*C

a + b + c = 180 and a* + b* + c =180 (a,b,a*,b,c are angles)

since both equations equal to 180, I equate them to each other and subtract angle c from both sides to get:

a + b = a* + b*.

I'm stuck here. I proved that their sum is the same, but not the angles. Do you have any suggestions?

Originally Posted by statmajor

I'm trying to prove that a=a* and b=b* using only the fact that the sum of the interior angles of a triangle is 180 degrees.

In my diagram, there are 2 triangles: ABC and A*B*C

a + b + c = 180 and a* + b* + c =180 (a,b,a*,b,c are angles)

since both equations equal to 180, I equate them to each other and subtract angle c from both sides to get:

a + b = a* + b*.

I'm stuck here. I proved that their sum is the same, but not the angles. Do you have any suggestions?

Is the line ab parallel to a*b*?

Yes, it is.

Originally Posted by statmajor

Yes, it is.

Because they are parallel, a=a* and b=b*.

What if I didn't know that the two lines were parallel?

What I'm tring to prove is that angles are congruent (using only the fact that the sum of the interior angles is 180). Would you know how?

I started what I thought was the correct method (my earlier post), but got stuck.

Originally Posted by statmajor

What if I didn't know that the two lines were parallel?

What I'm tring to prove is that angles are congruent (using only the fact that the sum of the interior angles is 180). Would you know how?

I started what I thought was the correct method (my earlier post), but got stuck.

I don't think you can get anywhere unless you know those two lines are paralle.